This is an interesting question that got a thorough investigation in the early 1980s, during the infamous Hitler Diaries fiasco. The German news magazine Stern, which had uncovered the – as things turned out, clumsily forged – diaries, was very concerned that the monumental scoop it thought it had on its hands might be disrupted by some distant heir of Hitler's, of whose existence it was unaware, coming forward to claim copyright over these materials. So it went to some effort to trace and negotiate with any likely claimants in advance.

The investigation was led by Dr Andreas Ruppert, the senior legal advisor at Stern's publisher, Gruner+Jahr, who reported back that "determining ownership of Hitler's estate was complex, indeed almost impossible." The facts, as established by Ruppert, were these:

• Hitler left a very brief personal will, which was appended to a much longer "political testament", in which he made a series of just three bequests. His art collection was to go to "a gallery" (unspecified) in Linz, personal possessions sufficient to "maintain a modest middle class standard of life" were to go to his Munich housekeeper, Frau Anni Winter, and the residue of his estate was willed to the Nazi party, or, failing that, to the state. Since the NSDAP was dissolved as a legal entity almost immediately afterwards, on 14 May 1945, by a decree of the Allied Military Government in Germany, the latter applied.
• As a result, Winter took away a trunk filled with personal mementoes such as Hitler's gun licence, his party membership card, and some paintings of his, from his Munich property.
• In 1948, the State of Bavaria brought a case against the late dictator's estate on the grounds that Hitler had been a resident of Berchtesgarden, and so it was the "state" referred to in his will. Bavaria won its case, and Hitler's will was then declared invalid in law. Bavaria subsequently confiscated about 5m marks owed to him in royalties on Mein Kampf and also acquired a claim to Hitler's surviving works of art. When Winter attempted to sell her trunk-load of Hitler's possessions to an American collector in 1951, the state sued to prevent this and confiscated the possessions.
• Several members of Hitler's family survived him, of whom the closest relative was his sister Paula Hiedler, who died in 1960 unmarried and childless. Paula signed an agreement soon after the war with a Swiss lawyer named François Genoud, himself a prominent Nazi, which allowed Genoud to press a claim that Paula, and not Bavaria, should be judged to have inherited a claim to the residue of Hitler's estate when the Nazi party was dissolved. Genoud, who had also been appointed literary executor of Joseph Goebbels and made substantial sums from the publication of the Goebbels diaries after they were located in a Soviet archive, made several attempts to claim copyright over Mein Kampf but was never able to press his case successfully in court.
• Other surviving members of the Hitler family also refused to accept the 1948 judgement, and made a separate agreement with a German historian named Werner Maser, to act as a trustee for its claims to Hitler's estate. Maser was a Hitler biographer with right-wing leanings who had in 1977 published a book attacking the Allies' conduct during the Nuremberg Trials.
• However, when publication of the conversations that made up Hitler's Table Talk took place in 1952, the Bavarian state discovered that, legally, the copyright it claimed on Hitler's writings extended only so far as it applied to writings published before the dictator's death. The state was unable to stop the publication of Table Talk.

Thus, when the diaries emerged in 1981, the legal status of Hitler's estate was that his will had been declared invalid, the State of Bavaria had been recognised as his heir to material effects and all published writings, but this status was still being disputed in court. In addition, the legal status of any unpublished writings was extremely hazy. G+J decided that Genoud was too disreputable a figure to have any dealings with, so it instead made a private agreement with Maser to get him onside for the planned publication of the diaries. Maser eventually signed an agreement on behalf of the Hitler family to renounce claims to any unpublished writings that might emerge in return for a payment of 20,000 marks. G+J also did a deal with the German state, in the form of the Bundesarchiv [Federal archives], which agreed to perform some tests on the diary pages, and not to challenge Stern's right to publish extracts on an exclusive basis, in exchange for the promise that the diaries would be donated to the archives once the publication (and profit-generating) cycle had run its course over a couple of years.

Source

Robert Harris, Selling Hitler (1987)

Much ended up in the state's hands, but much of the details ended up in court and weren't sorted out for many years to come. I've written previously about this here.